High School Understanding Causality in Quantum Mechanics

[mohamed amine]

can we find causality in quantum mechanic like the classical physics ?

 

[PeterDonis]

Moderator's note: moved to quantum physics forum.

 

[PeterDonis]

can we find causality in quantum mechanic like the classical physics ?

There is causality in QM, yes, although in some respects it doesn't work in quite the way you would expect from classical physics.

 

[DrChinese]

As PeterDonis says, causality in quantum physics does not follow some classical concepts. Specifically:

1. Measurement outcomes are expressed as an expected probability amplitude. The outcome of any specific measurement is random. There is no known "causal agent" responsible for that specific outcome. In the classical world, there is determinism in every outcome when the appropriate initial conditions are known.

2. The classical world is local realistic, while the quantum world is not. Trying to explain "local realistic" itself would be a separate topic, but here is a link that might help:

https://en.wikipedia.org/wiki/Principle_of_locality

 

[itfitmewelltoo]

As PeterDonis says, causality in quantum physics does not follow some classical concepts. Specifically:

1. Measurement outcomes are expressed as an expected probability amplitude. The outcome of any specific measurement is random. There is no known "causal agent" responsible for that specific outcome. In the classical world, there is determinism in every outcome when the appropriate setup parameters are known.

2. The classical world is local realistic, while the quantum world is not. Trying to explain "local realistic" itself would be a separate topic, but here is a link that might help:

https://en.wikipedia.org/wiki/Principle_of_locality

A specific example, please. For instance, photons are quantum particles. IR wavelengths or energy levels are absorbed by CO2. There are certain vibrational modes that are excited by this absorption. In the atmosphere, this energy may then be converted to kinetic energy of other molecules in the gas.

So there is a causal chain. If I am to understand this properly, this is a process that links the energy from the quantum physics of a photon to the classical physics of kinetic movement. Perhaps we need to go a step further and consider the gas to be contained in a piston, which will get us up to a more macroscopic level as the ideal gas law gives us PV=nRT, ergo we get classical work out of the system.

So, where in there do we see find the predominantly quantum physics (not so classical) process as you've described and the classical physics we are accustomed to?

 

[DrChinese]

A specific example, please. For instance, photons are quantum particles. IR wavelengths or energy levels are absorbed by CO2. There are certain vibrational modes that are excited by this absorption. In the atmosphere, this energy may then be converted to kinetic energy of other molecules in the gas.

So there is a causal chain. ...

So, where in there do we see find the predominantly quantum physics (not so classical) process as you've described and the classical physics we are accustomed to?

Almost anything related to a single photon will evidence quantum causality instead of classical causality. In your example of CO2 absorption, let's call it atmospheric CO2: That event occurs at a random time and place. If it originated from the sun, that photon could have appeared nearly anywhere in the Milky Way instead of that CO2 molecule. There is no known causal agent that induced that photon to come to Earth. I.e. there were no initial conditions that steered in this way.

You also could easily consider any demonstration of the Heisenberg Uncertainty relations to stand in opposition to the causality of the classical world.

 

[Mentz114]

can we find causality in quantum mechanic like the classical physics ?

As @DrChinese has said there is indeterminacy in quantum processes. But we can recover something like classical causality by summing many quantum effects. For instance with Brownian motion we can say that the motion of the pollen grain is caused by pressure fluctuations in the fluid. Those fluctuations are composed of many random molecular motions.

 

[vanhees71]

One has to clearly distinguish causality from determinism to get a clear picture how these notions have to be understood in the quantum realm. Causality is the prerequisite for making natural science possible at all, because it's the assumption that there are reproducible phenomena, i.e., if you do an experiment by preparing some particles to do, e.g., a scattering experiment the outcome always follows the same natural laws. If the natural laws would change randomly with time there'd be no natural sciences possible. That's why I think that causality is a prerequisite for the success of the natural sciences to describe phenomena and observations in nature by natural laws in terms of mathematical models/theories.

This already implies the definition of causality: A theory is causal if there is a description of states of a given system such that if the state of the system is known at times $t<t_0$, then the state is known (through some equations of motion, i.e., dynamical laws) at any later time $t>t_0$. This is the weak form causality and assumes a lot, namely the knowledge of the entire history of the system for times $t<t_0$. Fortunately nature is much more kind to us and seems to follow a stronger form of causality, at least on the fundamental level: It is sufficient to know the state of the system at one "initial time" $t_0$ to know it, given the dynamical laws, at any later time $t>t_0$.

This definition of causality holds for both classical and quantum physics. The fundamental difference between classical and quantum physics comes into the game when considering the question whether nature behaves deterministic. According to classical physics it does, but as experiments show classical physics is only an approximation valid for sufficiently "coarse-grained macroscopic observables", and quantum physics is an indeterministic theory, and this is a fact that can be observed by experiments, demonstrating the invalidity of Bell's inequality, at least under the assumption of locality of interactions.

So we have to think about determinism to get the fundamental difference between classical and quantum physics. A theory is deterministic if with the complete knowledge of the state of a system all possible observables of this system have definite values. Together with causality this implies that knowing the state at time $t_0$ (implying you know the values of all observables of the system exactly at this time) you know the precise state at any later time $t>t_0$ through the dynamical laws (implying you know the values of all observables of the system exactly at all these later times).

Take as an example classical point-particle mechanics: There the complete knowledge of the state implies to know all positions and momenta of each particles precisely, and given the forces acting on and among these particles you can know, given all positions and momenta at time $t_0$ precisely, all positions and momenta at any later time through the classical equations of motion (be it non-relativistic or relativistic).

Quantum theory however tells us that this is not possible. The precise knowledge of the quantum state (i.e., knowing that a system is in a given pure state $\hat{\rho}=|\psi \rangle \langle \psi |$) does not imply that you know the values of all possible observables precisely but only of those observables, which are presented by a (usually self-adjoint) operators in Hilbert space, for which $|\psi \rangle$ is an eigenvector. For all other observables you only know the probability to find one of its possible values when measuring it. Quantum theory is still causal, i.e., if you know the state of a system precisely at time $t=t_0$ you know it also precisely at all times $t>t_0$, given the Hamiltonian of the system and the solution of the quantum equations of motion for states and observables, but this doesn't imply the knowledge about all possible observables but only those mentioned above. Thus quantum theory is causal but indeterministic.

For an excellent comprehensive discussion of these mind-boggling issue, see

J. Schwinger, Quantum Mechanics - Symbolism of atomic measurements, Springer Verlag

 

[Derek P]

One has to clearly distinguish causality from determinism

Thank you for making a very clear distinction.

One point of confusion for many people may be that the bare word "determinism" could easily mean "determined by the past" rather than "determined from the present state". I have to confess I was not even aware of the useage and if pressed would probabaly have said that unitary evolution is deterministic - your definition would exclude the quantum state from being either deterministic or non-deterministic as the state itself is not observable. I can live with that.

I think there is another problem with causality. I could accept your definition, but in that case the idea of cause and effect becomes very elusive if the evolution is continuous. How do you pin down one state that the system passes through as the cause of what follows? Seems to have very little to do with A causing B.

edit - non-sequitur removed.